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. The homogeneous nucleation of ice in supercooled liquid-water clouds is characterized by time-dependent freezing rates. By contrast, water phase transitions induced heterogeneously by ice-nucleating particles (INPs) are described by time-independent ice-active fractions depending on ice supersaturation (s). Laboratory studies report ice-active particle number fractions (AFs) that are cumulative in s. Cloud models budget INP and ice crystal numbers to conserve total particle number during water phase transitions. Here, we show that ice formation from INPs with time-independent nucleation behavior is overpredicted when models budget particle numbers and at the same time derive ice crystal numbers from s-cumulative AFs. This causes a bias towards heterogeneous ice formation in situations where INPs compete with homogeneous droplet freezing during cloud formation. We resolve this issue by introducing differential AFs, thereby moving us one step closer to more robust simulations of aerosol–cloud interactions.

Aerosol–cloud interactions: the representation of heterogeneous ice activation in cloud models